Question 958600
the formula for the sum of the interior angles (S) of a regular polygon of n-sides:
{{{S = (n-2)180}}} 

if given that {{{S =  6840}}}, then we have

{{{6840 = (n-2)180}}} ...solve for {{{n}}}

{{{6840/180 = (n-2)180/180}}}

{{{38 = n-2}}}

{{{38+2 = n}}}

{{{n=40}}} a polygon called {{{tetracontahedron }}}